Optimization
Course Review
Teaching Evaluations
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– I highly value your feedback!
2
Role of this Course
• Provide preparation for
other courses in program
– Linear programming
– Comfort with Excel and
Solver
– Optimality conditions
• Provide an introduction
to the quantitative,
optimization way
– Modeling (variable,
objective, constraints)
– Analysis
– Technical expertise
– Analytical thinking
– Very useful for career!
• Specialize in this area
• Work with specialists
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Optimization in the Real World
Types of companies
• Small
– Specific optimization methods as specialization
– Consulting in niche market (employee scheduling,
gas/oil planning, finance, …)
• Large
– Optimization as essential need or as competitive
advantage
– Airline industry, automobile manufacturers,
Amazon.com, FedEx, Intel,…
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Commercial Software
• Linear and integer programming
– CPLEX
(by IBM/ILOG)
– XPRESS-MP (by Fico/Dash)
– Gurobi
(private company)
• Much faster, more robust than Solver
• Open source alternative: COIN-OR
– OpenSolver addIn for Excel
– better than Excel Solver, but not as good as
commercial software for more difficult problems
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Commercial Software (cont’d)
• Nonlinear programming
– No clear product
– Lots of specialized codes created
• Baron, Conopt, Minos,...
• Modeling software
– AIMMS, AMPL, GAMS, LINGO
– Much better than Excel
• Flexible, robust, scalable, better visualizations,…
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Optimization is increasing
• Optimization and Business Analytics are
becoming more pervasive
– From large companies only (1960s-80s) to running
Solver on your own laptop or iPhone
• Trends are moving towards more optimization
– Increased Data
– Faster Computers
– Better Algorithms
– Lower Fixed Cost (CPU, RAM, …)
– Service Applications
Course Topics
• Graphical method for LP
• LP terminology
– binding constraints, feasible
set,…
• LP modeling
– diet problem
– transportation problem
– assignment problem
– mixing/blending problems
• Sensitivity analysis
– shadow price, reduced cost, …
• Multiperiod LP problems
– shift scheduling, inventory
problems
• Spreadsheet modeling
• Simplex algorithm
– set up initial tableau, apply
pivoting steps
– introduce slack/surplus/artificial
variables
– two-phase method
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Course Topics (cont’d)
•
Network models
– network representation, network
flow LP
– minimum cost flow, maximum flow
models
– transportation, transshipment, shortest
path problem, tanker scheduling
•
Logic
– Truth Tables
– Quantifiers
•
Integer Programming
– modeling: logical constraints, fixed
costs, big-M
• Traveling Salesman Problem
– greedy heuristic, 2-exchange, IP
with subtour constraint generation
• Nonlinear Programming
– single variable optimization, multivariable optimization
– constrained optimization:
Lagrangians
– NLP with Excel
– sensitivity analysis
• Spreadsheet Modeling
– branch and bound
– applications: knapsack problem, set
covering, minimum order, facility
location/distribution, discount, index
fund
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Final exam
• The final exam will be cumulative
• You will not need Excel
• Calculators are allowed
• Open notes
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True False
• The optimal solution of a linear program is
unique if the final values of all the variables are
positive?
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True/ False
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True/False
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True/False
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True/False
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True/False
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True/False
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True/False
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Logic
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Logic
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Logic
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Integer Programming
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Integer Programming
• Variables?
• Objective?
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Integer Programming
• Constraint ensuring all waste is disposed?
• Constraint for respecting capacity and minimum
required shipment
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Integer Programming
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Networks
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Networks
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Networks
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Networks
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NLP
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NLP
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NLP
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NLP
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Sensitivity Analysis
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Sensitivity Analysis
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Sensitivity Analysis
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Sensitivity Analysis
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Sensitivity Analysis
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Sensitivity Analysis
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Sensitivity Analysis
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Sensitivity Analysis
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Sensitivity Analysis
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Multiperiod
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Multiperiod
• Variables?
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Multiperiod
• Objective?
• Constraints?
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Convexity/Concavity
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